The Karush–Kuhn–Tucker Optimality Conditions in Multiobjective Programming Problems with Interval-Valued Objective Functions. Wu, H. *European Journal of Operational Research*, 196(1):49–60, July, 2009. tex.ids: EJoOR-2009-Wu-KarushaPaper doi abstract bibtex The KKT conditions in multiobjective programming problems with interval-valued objective functions are derived in this paper. Many concepts of Pareto optimal solutions are proposed by considering two orderings on the class of all closed intervals. In order to consider the differentiation of an interval-valued function, we invoke the Hausdorff metric to deﬁne the distance between two closed intervals and the Hukuhara difference to deﬁne the difference of two closed intervals. Under these settings, we are able to consider the continuity and differentiability of an interval-valued function. The KKT optimality conditions can then be naturally elicited.

@article{wu_karushkuhntucker_2009,
title = {The {Karush}–{Kuhn}–{Tucker} {Optimality} {Conditions} in {Multiobjective} {Programming} {Problems} with {Interval}-{Valued} {Objective} {Functions}},
volume = {196},
issn = {03772217},
url = {https://linkinghub.elsevier.com/retrieve/pii/S0377221708002877},
doi = {10.1016/j.ejor.2008.03.012},
abstract = {The KKT conditions in multiobjective programming problems with interval-valued objective functions are derived in this paper. Many concepts of Pareto optimal solutions are proposed by considering two orderings on the class of all closed intervals. In order to consider the differentiation of an interval-valued function, we invoke the Hausdorff metric to deﬁne the distance between two closed intervals and the Hukuhara difference to deﬁne the difference of two closed intervals. Under these settings, we are able to consider the continuity and differentiability of an interval-valued function. The KKT optimality conditions can then be naturally elicited.},
language = {en},
number = {1},
urldate = {2022-01-19},
journal = {European Journal of Operational Research},
author = {Wu, Hsien-Chung},
month = jul,
year = {2009},
note = {tex.ids: EJoOR-2009-Wu-Karusha},
pages = {49--60},
}

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